I don’t know Mathjax well, and this isn’t even a released extension, so you’ll have to figure that out yourself, probably reaching out to the person who came up with that list of commands and asking them how to set things up (Franklin is not the problem here), note that in your example you’re still using KaTeX in your layout.
What I was suggesting is that this is just a bunch of fairly simple definition so you could just have these definitions yourself, I did the transformation of most of them:
Summary
\newcommand{\nthtop }[2]{\overset{#1}{#2}}
\newcommand{\joint }[1]{\overline{#1}}
\newcommand{\itop }[1]{\overset{1}{#1}}
\newcommand{\iitop }[1]{\overset{2}{#1}}
\newcommand{\iiitop }[1]{\overset{3}{#1}}
\newcommand{\ibottom }[1]{\underset{1}{#1}}
\newcommand{\iibottom }[1]{\underset{2}{#1}}
\newcommand{\iiibottom }[1]{\underset{3}{#1}}
\newcommand{\Ax}[2]{{A^{#1}_{#2}}}
\newcommand{\bAx}[2]{{\bar{A}^{#1}_{#2}}}
\newcommand{\dAx}[2]{{{\ddot A}^{#1}_{#2}}}
\newcommand{\tAx}[2]{{{\tilde A}^{#1}_{#2}}}
\newcommand{\ax}[2]{{a^{#1}_{#2}}}
\newcommand{\bax}[2]{{\bar{a}^{#1}_{#2}}}
\newcommand{\dax}[2]{{\ddot{a}^{#1}_{#2}}}
\newcommand{\tax}[2]{{\tilde{a}^{#1}_{#2}}}
\newcommand{\Aringx}[2]{{\mathring{A}^{#1}_{#2}}}
\newcommand{\aringx}[2]{{\mathring{a}^{#1}_{#2}}}
\newcommand{\Eringx}[2]{{\mathring{E}^{#1}_{#2}}}
\newcommand{\eringx}[2]{{\mathring{e}^{#1}_{#2}}}
\newcommand{\Sringx}[2]{{\mathring{S}^{#1}_{#2}}}
\newcommand{\sringx}[2]{{\mathring{s}^{#1}_{#2}}}
\newcommand{\dx }[2]{{d^{#1}_{#2}}}
\newcommand{\Dx }[2]{{\mathscr{D}^{#1}_{#2}}}
\newcommand{\IA }[0]{(IA)}
\newcommand{\IbA }[0]{(I\bar A)}
\newcommand{\bIbA }[0]{(\bar I\bar A)}
\newcommand{\ImA }[0]{(I^{(m)}A)}
\newcommand{\ImbA }[0]{(I^{(m)}\bar A)}
\newcommand{\bImbA }[0]{(\bar I^{(m)}\bar A)}
\newcommand{\Is }[0]{(Is)}
\newcommand{\Ibs }[0]{(I \bar s)}
\newcommand{\Ids }[0]{(I \ddot s)}
\newcommand{\Ex }[2]{{E^{#1}_{#2}}}
\newcommand{\DA }[0]{(DA)}
\newcommand{\DbA }[0]{(D\bar A)}
\newcommand{\bDbA }[0]{(\bar D\bar A)}
\newcommand{\DmA }[0]{(D^{(m)}A)}
\newcommand{\DmbA }[0]{(D^{(m)}\bar A)}
\newcommand{\bDmbA }[0]{(\bar D^{(m)}\bar A)}
\newcommand{\Ds }[0]{(Ds)}
\newcommand{\Dbs }[0]{(D \bar s)}
\newcommand{\Dds }[0]{(D \ddot s)}
\newcommand{\lx }[2]{{\ell^{#1}_{#2}}}
\newcommand{\Lx }[2]{{\mathscr{L}^{#1}_{#2}}}
\newcommand{\px }[2]{{p^{#1}_{#2}}}
\newcommand{\Px }[2]{{P^{#1}_{#2}}}
\newcommand{\premium }[2]{{P^{#1}\ \left({#2}\right)}}
\newcommand{\bpremium }[2]{{\bar{P}^{#1}\left({#2}\right)}}
\newcommand{\tpremium }[2]{{\tilde{P}^{#1}\left({#2}\right)}}
\newcommand{\paidup }[2]{{W^{#1}\ \left({#2}\right)}}
\newcommand{\bpaidup }[2]{{\bar{W}^{#1}\left({#2}\right)}}
\newcommand{\tpaidup }[2]{{\tilde{W}^{#1}\left({#2}\right)}}
\newcommand{\reserve }[2]{{V^{#1}\ \left({#2}\right)}}
\newcommand{\breserve }[2]{{\bar{V}^{#1}\left({#2}\right)}}
\newcommand{\treserve }[2]{{\tilde{V}^{#1}\left({#2}\right)}}
\newcommand{\qx }[2]{{q^{#1}_{#2}}}
\newcommand{\Qx }[2]{{Q^{#1}_{#2}}}
\newcommand{\sx}[2]{{s^{#1}_{#2}}}
\newcommand{\bsx}[2]{{\bar{s}^{#1}_{#2}}}
\newcommand{\dsx}[2]{{\ddot{s}^{#1}_{#2}}}
\newcommand{\Vx }[2]{{V^{#1}_{#2}}}
\newcommand{\Wx }[2]{{W^{#1}_{#2}}}
\newcommand{\actsymb }[5]{{_{#1}^{#2}{#3}_{#4}^{#5}}}
With those you can for instance do:
Summary
$$
\ax{}{\angl{K}} \\
\bax{}{P_t} \\
\bax{}{\angl{T}} \\
\bax{}{x}\\
\bax{h}{r} \\
\bax{i}{x+t}\\
\bax{r}{x+t}\\
\dax{}{\angl{K+1}}\\
\dax{(m)}{x}\\
$$
$$
\aringx{(m)}{x}\\
\dax{\{m\}}{x} \\\\
_j\dax{}{x} \\\\
_*\dax{}{x} \\\\
_{n|}\ax{}{x}\\\\
$$
$$
\Ax{}{xy} \\
\hat{B}_{x + t}^{(j)} \\
\actsymb{t}{}{D}{j}{}\\
$$
Note that in Franklin the number of arguments has to be respected precisely (as in LaTeX). Not sure why they don’t with their list. For instance the command \ax takes 2 arguments, so you have to provide two braces to it possibly leaving one empty.